This brief describes a multirate energy-bounding algorithm that significantly increases the displayable stiffness while guaranteeing the overall haptic interaction stability. Unlike haptic interaction control algorithms that are based on the multirate simulation of virtual environments, the proposed multirate approach separates the low-level control thread from the haptic thread. The haptic thread updates the haptic interaction computation, or the collision detection and response and dynamic or deformation simulation, of a virtual environment at slow rate while the low-level control thread updates the actuator command force determined by the energy-bounding algorithm to guarantee the interaction stability at a high update rate. An analytical derivation study shows that the displayable stiffness of virtual environments can be significantly increased by an order of N, which is the ratio of the fast actuator command signal update to the slow haptic simulation update. Experiments using a commercial haptic device demonstrate that the displayed stiffness significantly increases while guaranteeing stability even when the haptic rendering rate is slow.